Finite Group Databasebeta

← #13172348

Subgroups — #13172348

Order 1728.

1374 conjugacy classes of subgroups.

The subgroup lattice has 1196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723727C211yesmaximal, characteristic, complemented
2#11723626C211yesmaximal, characteristic, complemented
3#67⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
4C2×#88803C211yesmaximal, characteristic, complemented
5C3×#63981C211yesmaximal, characteristic, complemented
6C3×#63978C211yesmaximal, characteristic, complemented
7C3×#63964C211yesmaximal, characteristic, complemented
8#11723027C211yesmaximal, characteristic, complemented
9#11723025C211yesmaximal, characteristic, complemented
10#11723007C211yesmaximal, characteristic, complemented
11#11723001C211yesmaximal, characteristic, complemented
12#11722997C211yesmaximal, characteristic, complemented
13#11722990C211yesmaximal, characteristic, complemented
14#11722962C211yesmaximal, characteristic, complemented
15#11722955C211yesmaximal, characteristic, complemented
16#10595267—31nomaximal
17#10594979—31nomaximal
18#10594173—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C22×C32×Dic3C2211yescharacteristic
24C2×#6295C2211yescharacteristic
25C2×#6295C2211yescharacteristic
26C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
27C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
28C2×C3×#627C2211yescharacteristic, complemented
29C2×C3×#626C2211yescharacteristic
30C2×C3×#626C2211yescharacteristic
31C2×C3×#626C2211yescharacteristic, complemented
32C3×#3757C2211yescharacteristic
33C32×#217C2211yescharacteristic
34#88814C2211yescharacteristic
35#88814C2211yescharacteristic
36#88807C2211yescharacteristic, complemented
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
38#88803C2211yescharacteristic
39#88803C2211yescharacteristic
40#88803C2211yescharacteristic
41#88803C2211yescharacteristic
42#88803C2211yescharacteristic, complemented
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44Dic3×C3⋊Dic3C2211yescharacteristic, complemented
45Dic3×C3⋊Dic3C2211yescharacteristic, complemented
46C3×#3724C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×#3722C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54D4×C3⋊Dic3—31no—
55C2×#3752—31no—
56#64090—31no—
57C3×#939—31no—
58C3×#937—31no—
59C3×#930—31no—
60C3×#924—31no—
61C3×#882—31no—
62C3×#878—31no—
63#63981—31no—
64#63981D311yescharacteristic, complemented
65#63980—31no—
66#63978D311yescharacteristic, complemented
67#63977—31no—
68#63976—31no—
69#67⋊Dic3—31no—
70#67⋊Dic3—31no—
71#67⋊Dic3—31no—
72#67⋊Dic3—31no—
73#67⋊Dic3—61no—
74#67⋊Dic3—61no—
75#63970—31no—
76#63964D311yescharacteristic, complemented
77#63962—31no—
78C2×(C2×D3)⋊Dic3—31no—
79C2×(C2×D3)⋊Dic3—31no—
80C2×(C2×D3)⋊Dic3—61no—
81#63959—31no—
82#63916—31no—
83#63915—31no—
84#63907—31no—
85#63907—31no—
86#63907—31no—
87#63891—31no—
88#63890—31no—
89#63890—31no—
90#63886—31no—
91#63886—31no—
92#63886—31no—
93#63884—31no—
94#63863—31no—
95#63862—31no—
96#63862—31no—
97#63861—31no—
98#63858—31no—
99#63853—31no—
100#63848—31no—
101#63848—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3—22no—
104C22×C3×C3⋊D3—41no—
105C22×C3×C3⋊D3—41no—
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C3×C3⋊D3C2311yescharacteristic
109C22×C32×D3C2311yescharacteristic
110C2×C3⋊(C3⋊Dic3)—41no—
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
113C3×#638—22no—
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C32×#67—22no—
118C2×C32×Dic3—41no—
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124#6295—41no—
125#6295—41no—
126Dic3×C3⋊D3—41no—
127D3×C3⋊Dic3—41no—
128C3×#627—41no—
129C3×#626—41no—
130C3×#626—41no—
131C3×#626—41no—
132#5644—91no—
133#5617—91no—
134#5593—91no—
135C23×C3⋊D3C2×D311yescharacteristic
136C23×C3×D3—31no—
137C23×C3×D3—31no—
138C23×C3×D3—61no—
139C2×C32×D4—31no—
140C22×C32×C4—31no—
141C2×#638C2×D311yescharacteristic
142C22×C3⋊Dic3—31no—
143C22×C3⋊Dic3—31no—
144C22×C3⋊Dic3—31no—
145C22×C3⋊Dic3—31no—
146C22×C3⋊Dic3—61no—
147C22×C3⋊Dic3—61no—
148C22×C3⋊Dic3—61no—
149C22×C3⋊Dic3—121no—
150C2×C4×C3⋊D3—31no—
151C2×C3×#67—21no—
152C2×C3×#67—31no—
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C2×C3×#67—31no—
156C2×C3×#67—31no—
157C2×C3×#67—61no—
158C2×C3×#67C2×D311yescharacteristic
159C2×C3×#67C2×D311yescharacteristic
160C22×C3×Dic3—21no—
161C22×C3×Dic3C2×D311yescharacteristic
162C22×C3×Dic3C2×D311yescharacteristic
163C2×C3×D12—31no—
164C2×C3×D12—31no—
165C2×C3×D12—31no—
166C2×C3×Dic6—31no—
167C2×C3×Dic6—31no—
168C2×#627C2×D311yescharacteristic, complemented
169C2×#626—31no—
170C2×#626—31no—
171C2×#626—31no—
172C2×#626—31no—
173C2×#626C2×D311yescharacteristic
174C2×#626C2×D311yescharacteristic
175C2×#626C2×D311yescharacteristic, complemented
176C2×#625—31no—
177C2×#625—31no—
178C2×D3×Dic3—31no—
179C2×D3×Dic3—31no—
180C2×D3×Dic3—31no—
181C2×D3×Dic3—31no—
182C2×D3×Dic3—61no—
183C2×D3×Dic3—61no—
184C32×C22⋊C4—31no—
185#3757—31no—
186#3757C2×D311yescharacteristic
187#3752—31no—
188#3752—31no—
189#3752—31no—
190#3752—31no—
191#3752—31no—
192C4⋊(C3⋊Dic3)—31no—
193#3750—31no—
194C4×C3⋊Dic3—31no—
195C4×C3⋊Dic3—31no—
196C3×#217—21no—
197C3×#217—31no—
198C3×#217—31no—
199C3×#217—31no—
200C3×#217—61no—
201C3×#217C2×D311yescharacteristic
202C3×#217C2×D311yescharacteristic
203C3×(C2×D3)⋊C4—31no—
204C3×(C2×D3)⋊C4—31no—
205C3×(C2×D3)⋊C4—31no—
206C3×(C2×D3)⋊C4—31no—
207C3×(C2×D3)⋊C4—31no—
208C3×(C2×D3)⋊C4—31no—
209C3×(C2×D3)⋊C4—31no—
210C3×C4⋊Dic3—31no—
211C3×C4⋊Dic3—31no—
212C3×C4⋊Dic3—31no—
213C3×Dic3⋊C4—31no—
214C3×Dic3⋊C4—31no—
215C3×Dic3⋊C4—31no—
216C3×Dic3⋊C4—31no—
217C3×Dic3⋊C4—31no—
218#3724C2×D311yescharacteristic, complemented
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—61no—
224Dic3⋊Dic3—61no—
225Dic3⋊Dic3C2×D311yescharacteristic, complemented
226Dic3⋊Dic3C2×D311yescharacteristic, complemented
227Dic3⋊Dic3C2×D311yescharacteristic, complemented
228#3722—31no—
229#3722—31no—
230#3722C2×D311yescharacteristic
231#3722C2×D311yescharacteristic
232#3722C2×D311yescharacteristic, complemented
233(C2×D3)⋊Dic3—31no—
234(C2×D3)⋊Dic3—31no—
235(C2×D3)⋊Dic3—31no—
236(C2×D3)⋊Dic3—31no—
237(C2×D3)⋊Dic3—31no—
238(C2×D3)⋊Dic3—31no—
239(C2×D3)⋊Dic3—31no—
240(C2×D3)⋊Dic3—31no—
241(C2×D3)⋊Dic3—31no—
242(C2×D3)⋊Dic3—31no—
243(C2×D3)⋊Dic3—31no—
244(C2×D3)⋊Dic3—31no—
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—61no—
250(C2×D3)⋊Dic3—61no—
251(C2×D3)⋊Dic3—61no—
252(C2×D3)⋊Dic3—61no—
253(C2×D3)⋊Dic3—61no—
254(C2×D3)⋊Dic3—61no—
255(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
256Dic32—31no—
257Dic32—31no—
258Dic32—31no—
259Dic32—31no—
260Dic32—61no—
261Dic32—61no—
262C22×C33—21no—
263C22×C33—21no—
264C22×C33#4112yes—
265C22×C33C2411yescharacteristic
266C2×C3×C3⋊D3—21no—
267C2×C3×C3⋊D3—21no—
268C2×C3×C3⋊D3—21no—
269C2×C3×C3⋊D3—21no—
270C2×C3×C3⋊D3—21no—
271C2×C3×C3⋊D3—21no—
272C2×C3×C3⋊D3—21no—
273C2×C3×C3⋊D3—21no—
274C2×C3×C3⋊D3—21no—
275C2×C3×C3⋊D3—44no—
276C2×C32×D3—21no—
277C2×C32×D3—21no—
278C2×C32×D3—21no—
279C3⋊(C3⋊Dic3)—21no—
280C3⋊(C3⋊Dic3)—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C3×C3⋊Dic3—21no—
284C32×Dic3—21no—
285C32×Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3—21no—
288C32×Dic3—21no—
289C3×C22⋊Q8—91no—
290C3×#121—91no—
291C3×#120—91no—
292#953—91no—
293C2×#217—91no—
294#947—91no—
295#947—91no—
296#939—31no—
297#939—91no—
298#939—91no—
299#939—91no—
300#938—91no—
301#937—31no—
302#937—91no—
303#936—91no—
304#935—91no—
305D4×Dic3—91no—
306D4×Dic3—91no—
307D4×Dic3—91no—
308D4×Dic3—181no—
309#930—31no—
310C2×(C2×D3)⋊C4—91no—
311C2×(C2×D3)⋊C4—91no—
312C2×(C2×D3)⋊C4—181no—
313#924—31no—
314#898—91no—
315#898—91no—
316#898—91no—
317#898—91no—
318#895—91no—
319#895—91no—
320#894—91no—
321#894—91no—
322#886—91no—
323#886—91no—
324#885—91no—
325#885—91no—
326#885—91no—
327#883—91no—
328#882—31no—
329#882—91no—
330#67⋊C4—91no—
331#67⋊C4—91no—
332#67⋊C4—91no—
333#67⋊C4—181no—
334#879—91no—
335#879—91no—
336#878—31no—
337C23×C32—21no—
338C23×C32—21no—
339C23×C32—21no—
340C23×C32—31no—
341C23×C32—41no—
342C23×C32C22×D311yescharacteristic
343C23×C32C22×D311yescharacteristic
344C23×C32C22×D311yescharacteristic
345C22×C3⋊D3—22no—
346C22×C3⋊D3—41no—
347C22×C3⋊D3—41no—
348C22×C3⋊D3C22×D311yescharacteristic
349C22×C3⋊D3C22×D311yescharacteristic
350C22×C3⋊D3C22×D311yescharacteristic
351C22×C3×D3—21no—
352C22×C3×D3—31no—
353C22×C3×D3—31no—
354C22×C3×D3—31no—
355C22×C3×D3—31no—
356C22×C3×D3—31no—
357C22×C3×D3—31no—
358C22×C3×D3—61no—
359C22×C3×D3—61no—
360C22×C3×D3—61no—
361C22×C3×D3—64no—
362C22×C3×D3—62no—
363C22×C3×D3—62no—
364C22×C3×D3—121no—
365C22×C3×D3—121no—
366C22×C3×D3—121no—
367C22×C3×D3—121no—
368C22×C3×D3—122no—
369C22×C3×D3—122no—
370C22×C3×D3C22×D311yescharacteristic
371C22×C3×D3C22×D311yescharacteristic
372C32×D4—62no—
373C2×C32×C4—31no—
374C2×C32×C4—31no—
375C2×C32×C4—31no—
376C2×C32×C4—31no—
377C2×C32×C4—31no—
378C2×C32×C4—121no—
379#638—22no—
380C2×C3⋊Dic3—31no—
381C2×C3⋊Dic3—31no—
382C2×C3⋊Dic3—31no—
383C2×C3⋊Dic3—31no—
384C2×C3⋊Dic3—31no—
385C2×C3⋊Dic3—31no—
386C2×C3⋊Dic3—61no—
387C2×C3⋊Dic3—61no—
388C2×C3⋊Dic3—61no—
389C2×C3⋊Dic3—61no—
390C2×C3⋊Dic3—61no—
391C2×C3⋊Dic3—61no—
392C2×C3⋊Dic3—121no—
393C2×C3⋊Dic3—121no—
394C2×C3⋊Dic3—121no—
395C2×C3⋊Dic3—121no—
396C2×C3⋊Dic3—121no—
397C2×C3⋊Dic3—121no—
398C2×C3⋊Dic3—122no—
399C2×C3⋊Dic3—122no—
400C2×C3⋊Dic3—122no—
401C2×C3⋊Dic3—124no—
402C2×C3⋊Dic3C22×D311yescharacteristic
403C2×C3⋊Dic3C22×D311yescharacteristic
404C2×C3⋊Dic3C22×D311yescharacteristic
405C4×C3⋊D3—121no—
406C3×#67—24no—
407C3×#67—22no—
408C3×#67—22no—
409C3×#67—64no—
410C3×#67—62no—
411C3×#67—62no—
412C3×#67—121no—
413C3×#67—121no—
414C3×#67—121no—
415C2×C3×Dic3—21no—
416C2×C3×Dic3—21no—
417C2×C3×Dic3—21no—
418C2×C3×Dic3—21no—
419C2×C3×Dic3—21no—
420C2×C3×Dic3—31no—
421C2×C3×Dic3—31no—
422C2×C3×Dic3—31no—
423C2×C3×Dic3—31no—
424C2×C3×Dic3—31no—
425C2×C3×Dic3—31no—
426C2×C3×Dic3—41no—
427C2×C3×Dic3—41no—
428C2×C3×Dic3—42no—
429C2×C3×Dic3—61no—
430C2×C3×Dic3—61no—
431C2×C3×Dic3—61no—
432C2×C3×Dic3C22×D311yescharacteristic
433C2×C3×Dic3C22×D311yescharacteristic
434C2×C3×Dic3C22×D311yescharacteristic
435C2×C3×Dic3C22×D311yescharacteristic
436C2×C3×Dic3C22×D311yescharacteristic
437C2×C3×Dic3C22×D311yescharacteristic
438C2×C3×Dic3C22×D311yescharacteristic
439C2×C3×Dic3C22×D311yescharacteristic
440C2×C3×Dic3C22×D311yescharacteristic
441C2×C3×Dic3C22×D311yescharacteristic
442C3×D12—121no—
443C3×D12—121no—
444C3×D12—121no—
445C3×Dic6—121no—
446C3×Dic6—121no—
447#627—41no—
448#626—41no—
449#626—41no—
450#626—41no—
451#626—121no—
452#626—121no—
453#626—121no—
454#626—121no—
455#625—121no—
456#625—121no—
457D3×Dic3—121no—
458D3×Dic3—121no—
459D3×Dic3—122no—
460D3×Dic3—121no—
461D3×Dic3—121no—
462D3×Dic3—122no—
463#538—271noSylow
464C2×C33—22no—
465C2×C33C2×#4111yescharacteristic
466C2×C33H(5,𝔽2)11yescharacteristic
467C2×C33H(5,𝔽2)11yescharacteristic
468C3×C3⋊D3—41no—
469C3×C3⋊D3—41no—
470C3×C3⋊D3—41no—
471C32×D3—41no—
472C24×C3—91no—
473C23×D3—31no—
474C23×D3—31no—
475C23×D3—61no—
476C2×C3×Q8—91no—
477C2×C3×D4—31no—
478C2×C3×D4—31no—
479C2×C3×D4—61no—
480C2×C3×D4—91no—
481C2×C3×D4—91no—
482C2×C3×D4—91no—
483C2×C3×D4—91no—
484C22×C3×C4—31no—
485C22×C3×C4—31no—
486C22×C3×C4—61no—
487C2×#67—31no—
488C2×#67—31no—
489C2×#67—31no—
490C2×#67—31no—
491C2×#67—31no—
492C2×#67—61no—
493C2×#67—91no—
494C2×#67—91no—
495C2×#67—91no—
496C2×#67—91no—
497C2×#67D3211yescharacteristic
498C22×Dic3—91no—
499C22×Dic3—91no—
500C22×Dic3—91no—
501C22×Dic3—91no—
502C22×Dic3—91no—
503C22×Dic3—91no—
504C22×Dic3—181no—
505C22×Dic3—181no—
506C22×Dic3—181no—
507C22×Dic3—181no—
508C22×Dic3—361no—
509C22×Dic3D3211yescharacteristic
510C2×D12—31no—
511C2×D12—31no—
512C2×D12—31no—
513C2×D12—91no—
514C2×D12—91no—
515C2×C4×D3—91no—
516C2×C4×D3—91no—
517C2×C4×D3—91no—
518C2×C4×D3—181no—
519C2×Dic6—31no—
520C2×Dic6—31no—
521C3×C4⋊C4—91no—
522C3×C4⋊C4—91no—
523C3×C4⋊C4—91no—
524C3×C4⋊C4—91no—
525C3×C22⋊C4—31no—
526C3×C22⋊C4—31no—
527C3×C22⋊C4—61no—
528C3×C22⋊C4—91no—
529C3×C22⋊C4—91no—
530C3×C22⋊C4—91no—
531C3×C22⋊C4—91no—
532C3×C22⋊C4—91no—
533#217—31no—
534#217—31no—
535#217—31no—
536#217—61no—
537#217—91no—
538#217—91no—
539#217—91no—
540#217—91no—
541#217—91no—
542#217—91no—
543#217—91no—
544#217—91no—
545#217—91no—
546#217—181no—
547#217D3211yescharacteristic
548(C2×D3)⋊C4—31no—
549(C2×D3)⋊C4—31no—
550(C2×D3)⋊C4—31no—
551(C2×D3)⋊C4—31no—
552(C2×D3)⋊C4—31no—
553(C2×D3)⋊C4—31no—
554(C2×D3)⋊C4—31no—
555(C2×D3)⋊C4—91no—
556(C2×D3)⋊C4—91no—
557(C2×D3)⋊C4—91no—
558(C2×D3)⋊C4—91no—
559(C2×D3)⋊C4—91no—
560(C2×D3)⋊C4—91no—
561(C2×D3)⋊C4—91no—
562(C2×D3)⋊C4—91no—
563(C2×D3)⋊C4—91no—
564(C2×D3)⋊C4—91no—
565(C2×D3)⋊C4—91no—
566(C2×D3)⋊C4—91no—
567(C2×D3)⋊C4—91no—
568(C2×D3)⋊C4—91no—
569(C2×D3)⋊C4—91no—
570(C2×D3)⋊C4—181no—
571(C2×D3)⋊C4—181no—
572(C2×D3)⋊C4—181no—
573(C2×D3)⋊C4—181no—
574(C2×D3)⋊C4—181no—
575C4⋊Dic3—31no—
576C4⋊Dic3—31no—
577C4⋊Dic3—31no—
578C4⋊Dic3—91no—
579C4⋊Dic3—91no—
580C4⋊Dic3—91no—
581C4⋊Dic3—181no—
582Dic3⋊C4—31no—
583Dic3⋊C4—31no—
584Dic3⋊C4—31no—
585Dic3⋊C4—31no—
586Dic3⋊C4—31no—
587Dic3⋊C4—91no—
588Dic3⋊C4—91no—
589Dic3⋊C4—91no—
590Dic3⋊C4—181no—
591C4×Dic3—91no—
592C4×Dic3—91no—
593C4×Dic3—91no—
594C4×Dic3—91no—
595C4×Dic3—91no—
596C4×Dic3—91no—
597C4×Dic3—181no—
598C4×Dic3—181no—
599C22×C32—21no—
600C22×C32—21no—
601C22×C32—22no—
602C22×C32—22no—
603C22×C32—21no—
604C22×C32—21no—
605C22×C32—21no—
606C22×C32—21no—
607C22×C32—21no—
608C22×C32—21no—
609C22×C32—21no—
610C22×C32—22no—
611C22×C32—22no—
612C22×C32—22no—
613C22×C32—42no—
614C22×C32—41no—
615C22×C32—41no—
616C22×C32—41no—
617C22×C32—41no—
618C22×C32—41no—
619C22×C32—42no—
620C22×C32—42no—
621C22×C32—61no—
622C22×C32—61no—
623C22×C32—61no—
624C22×C32#23712yes—
625C22×C32#23712yes—
626C22×C32#23912yes—
627C22×C32C23×D311yescharacteristic
628C22×C32C23×D311yescharacteristic
629C22×C32C23×D311yescharacteristic
630C2×C3⋊D3—21no—
631C2×C3⋊D3—21no—
632C2×C3⋊D3—21no—
633C2×C3⋊D3—21no—
634C2×C3⋊D3—21no—
635C2×C3⋊D3—21no—
636C2×C3⋊D3—21no—
637C2×C3⋊D3—21no—
638C2×C3⋊D3—21no—
639C2×C3⋊D3—44no—
640C2×C3×D3—22no—
641C2×C3×D3—21no—
642C2×C3×D3—21no—
643C2×C3×D3—21no—
644C2×C3×D3—21no—
645C2×C3×D3—21no—
646C2×C3×D3—21no—
647C2×C3×D3—41no—
648C2×C3×D3—41no—
649C2×C3×D3—62no—
650C2×C3×D3—62no—
651C2×C3×D3—62no—
652C2×C3×D3—61no—
653C2×C3×D3—61no—
654C2×C3×D3—61no—
655C2×C3×D3—61no—
656C2×C3×D3—61no—
657C2×C3×D3—61no—
658C2×C3×D3—61no—
659C2×C3×D3—61no—
660C2×C3×D3—61no—
661C2×C3×D3—61no—
662C2×C3×D3—61no—
663C2×C3×D3—61no—
664C2×C3×D3—61no—
665C2×C3×D3—61no—
666C2×C3×D3—61no—
667C2×C3×D3—61no—
668C2×C3×D3—61no—
669C2×C3×D3—61no—
670C2×C3×D3—121no—
671C2×C3×D3—121no—
672C2×C3×D3—121no—
673C2×C3×D3—121no—
674C2×C3×D3—121no—
675C2×C3×D3—121no—
676C2×C3×D3—128no—
677C2×C3×D3—124no—
678C2×C3×D3—124no—
679C32×C4—61no—
680C32×C4—61no—
681C32×C4—61no—
682C32×C4—61no—
683C32×C4—61no—
684C3⋊Dic3—21no—
685C3⋊Dic3—21no—
686C3⋊Dic3—21no—
687C3⋊Dic3—61no—
688C3⋊Dic3—61no—
689C3⋊Dic3—62no—
690C3⋊Dic3—62no—
691C3⋊Dic3—61no—
692C3⋊Dic3—61no—
693C3⋊Dic3—61no—
694C3⋊Dic3—61no—
695C3⋊Dic3—121no—
696C3⋊Dic3—121no—
697C3⋊Dic3—121no—
698C3⋊Dic3—121no—
699C3⋊Dic3—122no—
700C3⋊Dic3—122no—
701C3×Dic3—22no—
702C3×Dic3—21no—
703C3×Dic3—21no—
704C3×Dic3—21no—
705C3×Dic3—21no—
706C3×Dic3—21no—
707C3×Dic3—21no—
708C3×Dic3—21no—
709C3×Dic3—21no—
710C3×Dic3—21no—
711C3×Dic3—21no—
712C3×Dic3—41no—
713C3×Dic3—41no—
714C3×Dic3—41no—
715C3×Dic3—41no—
716C3×Dic3—62no—
717C3×Dic3—61no—
718C3×Dic3—61no—
719C3×Dic3—61no—
720C3×Dic3—61no—
721C3×Dic3—61no—
722C3×Dic3—61no—
723C3×Dic3—121no—
724C3×Dic3—121no—
725#126—271no—
726#126—271no—
727#124—271no—
728#124—271no—
729#123—271no—
730#123—271no—
731C22⋊Q8—91no—
732#121—91no—
733#121—271no—
734#121—271no—
735#120—91no—
736#120—271no—
737C4×D4—271no—
738C4×D4—271no—
739C2×C22⋊C4—271no—
740C33#53811yescharacteristic, complemented, Sylow
741C23×C3—21no—
742C23×C3—21no—
743C23×C3—21no—
744C23×C3—31no—
745C23×C3—31no—
746C23×C3—41no—
747C23×C3—61no—
748C23×C3—91no—
749C23×C3—91no—
750C23×C3—91no—
751C23×C3—182no—
752C23×C3—361no—
753C23×C3—361no—
754C23×C3C2×D3211yescharacteristic
755C23×C3C2×D3211yescharacteristic
756C23×C3C2×D3211yescharacteristic
757C22×D3—31no—
758C22×D3—31no—
759C22×D3—31no—
760C22×D3—31no—
761C22×D3—31no—
762C22×D3—31no—
763C22×D3—61no—
764C22×D3—61no—
765C22×D3—61no—
766C22×D3—64no—
767C22×D3—62no—
768C22×D3—62no—
769C22×D3—121no—
770C22×D3—121no—
771C22×D3—121no—
772C22×D3—121no—
773C22×D3—122no—
774C22×D3—122no—
775C22×D3C2×D3211yescharacteristic
776C3×Q8—361no—
777C3×D4—64no—
778C3×D4—62no—
779C3×D4—62no—
780C3×D4—182no—
781C3×D4—361no—
782C3×D4—361no—
783C3×D4—361no—
784C2×C3×C4—31no—
785C2×C3×C4—31no—
786C2×C3×C4—31no—
787C2×C3×C4—31no—
788C2×C3×C4—31no—
789C2×C3×C4—31no—
790C2×C3×C4—31no—
791C2×C3×C4—31no—
792C2×C3×C4—31no—
793C2×C3×C4—31no—
794C2×C3×C4—61no—
795C2×C3×C4—61no—
796C2×C3×C4—61no—
797C2×C3×C4—61no—
798C2×C3×C4—61no—
799C2×C3×C4—91no—
800C2×C3×C4—91no—
801C2×C3×C4—91no—
802C2×C3×C4—121no—
803C2×C3×C4—121no—
804C2×C3×C4—122no—
805#67—22no—
806#67—64no—
807#67—62no—
808#67—62no—
809#67—121no—
810#67—121no—
811#67—121no—
812#67—361no—
813#67—361no—
814#67—361no—
815#67—361no—
816C2×Dic3—31no—
817C2×Dic3—31no—
818C2×Dic3—31no—
819C2×Dic3—31no—
820C2×Dic3—31no—
821C2×Dic3—31no—
822C2×Dic3—41no—
823C2×Dic3—61no—
824C2×Dic3—61no—
825C2×Dic3—61no—
826C2×Dic3—91no—
827C2×Dic3—91no—
828C2×Dic3—91no—
829C2×Dic3—91no—
830C2×Dic3—91no—
831C2×Dic3—91no—
832C2×Dic3—181no—
833C2×Dic3—181no—
834C2×Dic3—181no—
835C2×Dic3—181no—
836C2×Dic3—181no—
837C2×Dic3—181no—
838C2×Dic3—361no—
839C2×Dic3—361no—
840C2×Dic3—361no—
841C2×Dic3—361no—
842C2×Dic3—361no—
843C2×Dic3—362no—
844C2×Dic3—361no—
845C2×Dic3—361no—
846C2×Dic3—361no—
847C2×Dic3—362no—
848C2×Dic3—362no—
849C2×Dic3—362no—
850C2×Dic3—364no—
851C2×Dic3C2×D3211yescharacteristic
852C2×Dic3C2×D3211yescharacteristic
853C2×Dic3C2×D3211yescharacteristic
854C2×Dic3C2×D3211yescharacteristic
855C2×Dic3C2×D3211yescharacteristic
856D12—121no—
857D12—121no—
858D12—121no—
859D12—361no—
860D12—361no—
861C4×D3—361no—
862C4×D3—361no—
863C4×D3—362no—
864C4×D3—361no—
865Dic6—121no—
866Dic6—121no—
867C2×C32—22no—
868C2×C32—24no—
869C2×C32—22no—
870C2×C32—22no—
871C2×C32—21no—
872C2×C32—21no—
873C2×C32—21no—
874C2×C32—21no—
875C2×C32—21no—
876C2×C32—21no—
877C2×C32—21no—
878C2×C32—21no—
879C2×C32—21no—
880C2×C32—41no—
881C2×C32—41no—
882C2×C32—41no—
883C2×C32—42no—
884C2×C32—42no—
885C2×C32—44no—
886C2×C32—121no—
887C2×C32C2×#23711yescharacteristic
888C2×C32C2×#23711yescharacteristic
889C2×C32#100411yescharacteristic
890C2×C32#100411yescharacteristic
891C2×C32#100411yescharacteristic
892C2×C32#100411yescharacteristic
893C2×C32C2×#23911yescharacteristic
894C2×C32#100911yescharacteristic
895C2×C32#100911yescharacteristic
896C3⋊D3—41no—
897C3⋊D3—41no—
898C3⋊D3—41no—
899C3×D3—42no—
900C3×D3—41no—
901C3×D3—41no—
902C3×D3—122no—
903C3×D3—122no—
904C3×D3—122no—
905C3×D3—121no—
906C3×D3—121no—
907C3×D3—121no—
908C3×D3—121no—
909C3×D3—121no—
910C3×D3—121no—
911C24—91no—
912C2×Q8—91no—
913C2×D4—31no—
914C2×D4—91no—
915C2×D4—91no—
916C2×D4—91no—
917C2×D4—91no—
918C2×D4—271no—
919C2×D4—271no—
920C22×C4—31no—
921C22×C4—271no—
922C22×C4—271no—
923C22×C4—271no—
924C4⋊C4—91no—
925C4⋊C4—91no—
926C4⋊C4—91no—
927C4⋊C4—91no—
928C4⋊C4—271no—
929C4⋊C4—271no—
930C22⋊C4—31no—
931C22⋊C4—91no—
932C22⋊C4—91no—
933C22⋊C4—91no—
934C22⋊C4—91no—
935C22⋊C4—91no—
936C22⋊C4—271no—
937C22⋊C4—271no—
938C22⋊C4—271no—
939C22⋊C4—271no—
940C22⋊C4—271no—
941C22⋊C4—271no—
942C22⋊C4—271no—
943C22⋊C4—271no—
944C42—271no—
945C42—271no—
946C22×C3—22no—
947C22×C3—22no—
948C22×C3—21no—
949C22×C3—21no—
950C22×C3—21no—
951C22×C3—21no—
952C22×C3—21no—
953C22×C3—21no—
954C22×C3—21no—
955C22×C3—21no—
956C22×C3—21no—
957C22×C3—22no—
958C22×C3—22no—
959C22×C3—22no—
960C22×C3—41no—
961C22×C3—41no—
962C22×C3—41no—
963C22×C3—41no—
964C22×C3—42no—
965C22×C3—42no—
966C22×C3—41no—
967C22×C3—42no—
968C22×C3—62no—
969C22×C3—61no—
970C22×C3—61no—
971C22×C3—61no—
972C22×C3—61no—
973C22×C3—61no—
974C22×C3—61no—
975C22×C3—121no—
976C22×C3—121no—
977C22×C3—181no—
978C22×C3—181no—
979C22×C3—181no—
980C22×C3—181no—
981C22×C3—181no—
982C22×C3—181no—
983C22×C3—181no—
984C22×C3—181no—
985C22×C3—181no—
986C22×C3—364no—
987C22×C3#379612yes—
988C22×C3#379612yes—
989C22×C3#380512yes—
990C22×C3C22×D3211yescharacteristic
991C22×C3C22×D3211yescharacteristic
992C22×C3C22×D3211yescharacteristic
993C2×D3—21no—
994C2×D3—21no—
995C2×D3—21no—
996C2×D3—62no—
997C2×D3—62no—
998C2×D3—62no—
999C2×D3—61no—
1000C2×D3—61no—
1001C2×D3—61no—
1002C2×D3—61no—
1003C2×D3—61no—
1004C2×D3—61no—
1005C2×D3—61no—
1006C2×D3—61no—
1007C2×D3—61no—
1008C2×D3—61no—
1009C2×D3—61no—
1010C2×D3—61no—
1011C2×D3—61no—
1012C2×D3—61no—
1013C2×D3—61no—
1014C2×D3—61no—
1015C2×D3—61no—
1016C2×D3—61no—
1017C2×D3—121no—
1018C2×D3—121no—
1019C2×D3—121no—
1020C2×D3—121no—
1021C2×D3—121no—
1022C2×D3—121no—
1023C2×D3—128no—
1024C2×D3—124no—
1025C2×D3—124no—
1026C3×C4—62no—
1027C3×C4—61no—
1028C3×C4—61no—
1029C3×C4—61no—
1030C3×C4—61no—
1031C3×C4—61no—
1032C3×C4—61no—
1033C3×C4—61no—
1034C3×C4—61no—
1035C3×C4—61no—
1036C3×C4—61no—
1037C3×C4—121no—
1038C3×C4—121no—
1039C3×C4—121no—
1040C3×C4—121no—
1041C3×C4—181no—
1042C3×C4—181no—
1043C3×C4—181no—
1044Dic3—21no—
1045Dic3—21no—
1046Dic3—21no—
1047Dic3—21no—
1048Dic3—21no—
1049Dic3—62no—
1050Dic3—61no—
1051Dic3—61no—
1052Dic3—61no—
1053Dic3—61no—
1054Dic3—61no—
1055Dic3—61no—
1056Dic3—121no—
1057Dic3—121no—
1058Dic3—182no—
1059Dic3—182no—
1060Dic3—181no—
1061Dic3—181no—
1062Dic3—181no—
1063Dic3—181no—
1064Dic3—181no—
1065Dic3—181no—
1066Dic3—361no—
1067Dic3—361no—
1068Dic3—361no—
1069Dic3—361no—
1070Dic3—362no—
1071Dic3—362no—
1072C32—21no—
1073C32—21no—
1074C32—21no—
1075C32—41no—
1076C32#559311yescharacteristic, complemented
1077C32#561711yescharacteristic, complemented
1078C32#564411yescharacteristic, complemented
1079C23—31no—
1080C23—91no—
1081C23—91no—
1082C23—91no—
1083C23—182no—
1084C23—361no—
1085C23—361no—
1086C23D3311yescharacteristic
1087Q8—361no—
1088D4—62no—
1089D4—182no—
1090D4—361no—
1091D4—361no—
1092D4—361no—
1093D4—1081no—
1094D4—1081no—
1095C2×C4—31no—
1096C2×C4—31no—
1097C2×C4—31no—
1098C2×C4—31no—
1099C2×C4—31no—
1100C2×C4—91no—
1101C2×C4—91no—
1102C2×C4—91no—
1103C2×C4—121no—
1104C2×C4—271no—
1105C2×C4—271no—
1106C2×C4—1081no—
1107C2×C4—1081no—
1108C2×C4—1081no—
1109C2×C3—24no—
1110C2×C3—22no—
1111C2×C3—22no—
1112C2×C3—22no—
1113C2×C3—21no—
1114C2×C3—21no—
1115C2×C3—21no—
1116C2×C3—21no—
1117C2×C3—21no—
1118C2×C3—21no—
1119C2×C3—21no—
1120C2×C3—21no—
1121C2×C3—21no—
1122C2×C3—42no—
1123C2×C3—42no—
1124C2×C3—44no—
1125C2×C3—41no—
1126C2×C3—41no—
1127C2×C3—41no—
1128C2×C3—122no—
1129C2×C3—121no—
1130C2×C3—121no—
1131C2×C3—361no—
1132C2×C3—361no—
1133C2×C3—361no—
1134C2×C3C2×#379611yescharacteristic
1135C2×C3C2×#379611yescharacteristic
1136C2×C3#6430811yescharacteristic
1137C2×C3#6431311yescharacteristic
1138C2×C3#6431311yescharacteristic
1139C2×C3#6431411yescharacteristic
1140C2×C3#6431411yescharacteristic
1141C2×C3C2×#380511yescharacteristic
1142C2×C3#6433011yescharacteristic
1143D3—41no—
1144D3—122no—
1145D3—122no—
1146D3—122no—
1147D3—121no—
1148D3—121no—
1149D3—121no—
1150D3—121no—
1151D3—121no—
1152D3—121no—
1153C22—21no—
1154C22—21no—
1155C22—61no—
1156C22—61no—
1157C22—61no—
1158C22—181no—
1159C22—181no—
1160C22—181no—
1161C22—181no—
1162C22—181no—
1163C22—181no—
1164C22—181no—
1165C22—181no—
1166C22—181no—
1167C22—364no—
1168C22#8896412yes—
1169C22C2×D3311yescharacteristic
1170C4—61no—
1171C4—61no—
1172C4—61no—
1173C4—61no—
1174C4—61no—
1175C4—181no—
1176C4—181no—
1177C4—181no—
1178C4—541no—
1179C4—541no—
1180C3—21no—
1181C3—21no—
1182C3—21no—
1183C3—41no—
1184C3#1059417311yescharacteristic, complemented
1185C3#1059497911yescharacteristic, complemented
1186C3#1059526711yescharacteristic, complemented
1187C2—22no—
1188C2—121no—
1189C2—361no—
1190C2—361no—
1191C2—361no—
1192C2#1172441511yescharacteristic
1193C2#1172442011yescharacteristic
1194C2C2×#8896411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#538
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #11723727C2semidirect
2. #11723626C2semidirect
3. #67⋊(C3⋊Dic3)C2semidirect
4. C2×#88803C2semidirect
5. C3×#63981C2semidirect
6. C3×#63978C2semidirect
7. C3×#63964C2semidirect
8. #11723027C2semidirect
9. #11723025C2semidirect
10. #11723007C2semidirect
11. #11723001C2semidirect
12. #11722997C2semidirect
13. #11722990C2semidirect
14. #11722962C2semidirect
15. #11722955C2semidirect
26. C2×Dic3×C3⋊D3C22semidirect
27. C2×D3×C3⋊Dic3C22semidirect
28. C2×C3×#627C22semidirect
31. C2×C3×#626C22semidirect
36. #88807C22semidirect
37. Dic3⋊(C3⋊Dic3)C22semidirect
42. #88803C22semidirect
43. (C2×D3)⋊(C3⋊Dic3)C22semidirect
44. Dic3×C3⋊Dic3C22semidirect
45. Dic3×C3⋊Dic3C22semidirect
46. C3×#3724C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
52. C3×#3722C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
64. #63981D3semidirect
66. #63978D3semidirect
76. #63964D3semidirect
168. C2×#627C2×D3semidirect
175. C2×#626C2×D3semidirect
218. #3724C2×D3semidirect
225. Dic3⋊Dic3C2×D3semidirect
226. Dic3⋊Dic3C2×D3semidirect
227. Dic3⋊Dic3C2×D3semidirect
232. #3722C2×D3semidirect
255. (C2×D3)⋊Dic3C2×D3semidirect
740. C33#538semidirect
1076. C32#5593semidirect
1077. C32#5617semidirect
1078. C32#5644semidirect
1184. C3#10594173semidirect
1185. C3#10594979semidirect
1186. C3#10595267semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#117237272
#117236262
#67⋊(C3⋊Dic3)2
C2×#888032
C3×#639812
C3×#639782
C3×#639642
#117230272
#117230252
#117230072
#117230012
#117229972
#117229902
#117229622
#117229552
#105952673
#105949793
#105941733